# Evaluate some limits

Provide some guidance in approaching the following question:

let c denote a complex constant

then show that :

lim (z^2 + c) = z0^2 +c

z->z0.

https://brainmass.com/math/real-analysis/evaluate-limits-479461

#### Solution Preview

Proof. Let z=x+iy, z0=x0+iy0 and c=a+ib. Suppose that f(z)=u(x,y)+iv(x,y), where u(x,y) and v(x,y) are real functions in terms of x and y. Then

lim f(z) = lim u(x,y)+iv(x,y) ............................(1)

z->z0 ...

#### Solution Summary

The solution assesses limits of complex functions.

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